# A fair die is thrown two times. Find the probability that sum of the numbers on them is at least 8 - Mathematics and Statistics

Sum

A fair die is thrown two times. Find the probability that sum of the numbers on them is at least 8

#### Solution

When a fair die is tossed twice, the sample sp ace S is given by

S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

∴ n(S) = 36

Let B = event that sum of numbers is at least 8

∴ B = {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2), (3, 6), (4, 5), (5, 4), (6, 3), (4, 6), (5, 5), (6, 4), (5, 6), (6, 5), (6, 6)}

∴ n(B) = 15

∴ P(B) = ("n"("B"))/("n"("S"))

= 15/36

= 5/12

Concept: Concept of Probability
Is there an error in this question or solution?